1. HAWKES LEARNING SYSTEMS math courseware specialists Copyright © 2011 Hawkes Learning Systems. All rights reserved. Hawkes Learning Systems: Developmental Mathematics Section 14.6: Rational Exponents

2. HAWKES LEARNING SYSTEMS math courseware specialists Copyright © 2011 Hawkes Learning Systems. All rights reserved. Rational Exponents of the Form Summary of the Rules for Exponents For nonzero real numbers a and b and rational numbers m and n, The exponent 1: a  a 1 (a is any real number.) The exponent 0: a 0  1 (a  0) The product rule: a m ∙ a n  a m  n The quotient rule:

3. HAWKES LEARNING SYSTEMS math courseware specialists Copyright © 2011 Hawkes Learning Systems. All rights reserved. Rational Exponents of the Form (cont.) Summary of the Rules for Exponents (cont.) Negative exponents: Power rule: (a m ) n  a mn Power of a product: (ab) n  a n b n Power of a quotient:

4. HAWKES LEARNING SYSTEMS math courseware specialists Copyright © 2011 Hawkes Learning Systems. All rights reserved. Rational Exponents of the Form The General Form If n is a positive integer, m is any integer, and is a real number, then In radical notation:

5. HAWKES LEARNING SYSTEMS math courseware specialists Copyright © 2011 Hawkes Learning Systems. All rights reserved. Evaluating Principal n th Roots a. because 7 2  49. b. because 3 4  81. c. because (  2) 3   8. d. because (0.1) 5  0.00001. e. is not a real number. Any even root of a negative number is nonreal.

6. HAWKES LEARNING SYSTEMS math courseware specialists Copyright © 2011 Hawkes Learning Systems. All rights reserved. Conversion Between Exponential Notation and Radical Notation Assume that each variable represents a positive real number. Each expression is changed to an equivalent expression in either radical or exponential notation.

7. HAWKES LEARNING SYSTEMS math courseware specialists Copyright © 2011 Hawkes Learning Systems. All rights reserved. Conversion Between Exponential Notation and Radical Notation

8. HAWKES LEARNING SYSTEMS math courseware specialists Copyright © 2011 Hawkes Learning Systems. All rights reserved. Each expression is simplified using one or more of the rules for exponents.

9. HAWKES LEARNING SYSTEMS math courseware specialists Copyright © 2011 Hawkes Learning Systems. All rights reserved. Simplifying Expressions with Rational Exponents

10. HAWKES LEARNING SYSTEMS math courseware specialists Copyright © 2011 Hawkes Learning Systems. All rights reserved. Simplifying Expressions with Rational Exponents

11. HAWKES LEARNING SYSTEMS math courseware specialists Copyright © 2011 Hawkes Learning Systems. All rights reserved. Simplifying Radical Notation by Changing to Exponential Notation Simplify each expression by first changing it into an equivalent expression with rational exponents. Then rewrite the answer in simplified radical form.

12. HAWKES LEARNING SYSTEMS math courseware specialists Copyright © 2011 Hawkes Learning Systems. All rights reserved. Simplifying Radical Notation by Changing to Exponential Notation